Based on the plane equivalent pitch curve of elliptical bevel gear，the pressure angle in the transmission is acquired with differential geometry and gear meshing theories. The force analysis in the meshing process is performed and the formulas of tangential force and normal force on the gear teeth are derived. A method to calculate elliptical bevel gear’s strength in a successive way is established and the regulation of the tooth surface contacting stress and the root bending stress changing with the angle of driving gear is discussed. Then the position of the weakest tooth is determined and the influence of basic parameters including module，number of teeth and eccentricity ratio on contacting stress and bending stress is analysed. Comparing with traditional calculation for spur bevel gear，the exactness of this successive strength calculation method is verified.